Minimizing pressure sensitivity of optical fibers is important where they are used as leads to sensors and as reference fibers. In optical fiber acoustic sensors it is desirable to localize the fiber sensitivity by making the lead optical fibers pressure insensitive. In other optical fiber sensors (e.g. magnetic, and temperature), it is desirable to desensitize the fiber including even the sensing area to acoustic wave pressures because such acts as a noise source. It is important to localize the fiber's sensitivity to a desired area.
Sensitivity of an optical fiber waveguide is governed by elastic and elasto-optic coefficient of the optical fiber, the elastic coefficient of the coating and the thickness of the various layers. There are combinations of glass and coating materials and corresponding thicknesses which make optical fiber waveguides pressure insensitive. Generally, as the bulk modulus of the coating material increases, the sensitivity of the optical fiber decreases. There are disclosed combinations of glass and buffer materials and thicknesses which result in near zero pressure sensitivity. The pressure sensitivity of the optical phase in a fiber is defined as the magnitude of .DELTA..phi./.phi..DELTA.P, where .DELTA..phi. is the shift in the phase delay .phi. due to a pressure change .DELTA.P. If a given pressure change, .DELTA.P, results in a fiber core axial strain .epsilon..sub.z and radial strain .epsilon..sub.r, then it can be shown that ##EQU1## Here P.sub.11 and P.sub.12 are the elasto-optic or Pockels coefficients of the core and n is the refractive index of the core. The first term in Eq. (1) is the part of .DELTA..phi./.phi..DELTA.P which is due to the fiber length change, while the second and third terms are the parts due to the refractive index modulation of the core, which is related to the photoelastic effect. Stated another way .DELTA..phi./.phi..DELTA.P=the algebraic sum of the phase change due to the fiber length change plus phase change due to refractive index change. The objective is to have .DELTA..phi./.phi..DELTA.P=0. When .DELTA..phi./.phi..DELTA.P is zero the fiber is insensitive.
A typical optical fiber (FIG. 2a) is composed of a core, cladding, and a substrate from glasses having similar properties. This glass fiber is usually coated with a soft rubber and then with a hard plastic. In order to calculate the sensitivity as given in Eq. (1) the strains in the core .epsilon..sub.z and .epsilon..sub.r must be related to properties of the various layers of the fiber. The pressure sensitivity of a fiber with one layer or two layers has already been reported. In the present analysis we have taken into account the exact geometry of a typical four layer fiber, as shown in FIG. 2a.
The polar stresses .sigma..sub.r, .sigma..sub..theta., and .sigma..sub.z in the fiber are related to the strains .epsilon..sub.r, .epsilon..sub..theta., and .epsilon..sub.z as follows: ##EQU2## where i is the layer index, (0 for the core, 1 for the cladding, etc.) and .lambda..sup.i and .mu..sup.i are the Lame parameters which are related to the Young's modulus, E.sup.i, and Poisson's ratio, .nu..sup.i, as follows: ##EQU3##
For a cylinder the strains can be obtained from the Lame solutions ##EQU4## where U.sub.o.sup.i, U.sub.l.sup.i and W.sub.o.sup.i are constants to be determined. Since the strains must be finite at the center of the core, U.sub.l.sup.o =0.
For a fiber with m layers, the constants U.sub.o.sup.i, U.sub.l.sup.i, and W.sub.o.sup.i in Eq. (4) are determined from the boundary conditions: ##EQU5## where u.sub.r.sup.i (=.intg..epsilon..sub.r.sup.i dr) is the radial displacement in the i.sup.th layer, and r.sub.i and A.sub.i are the radius and the cross section area of the i.sup.th layer, respectively. Equations (5) and (6) describe the radial stress and displacement continuity across the boundaries of the layers. Equations (7) and (8) assume that the applied pressure is hydrostatic. Equation (9) is the plane strain approximation which ignores end effects. For long thin cylinders, such as fibers, it introduces an error of less than 1%. Using the boundary conditions described by Eqs. (5)-(9), the constants U.sub.o.sup.i, U.sub.l.sup.i, and W.sub.o.sup.i are determined and .epsilon..sub.r.sup.o and .epsilon..sub.z.sup.o are calculated from Eq. (4). Then, from Eq. (1) the sensitivity, .DELTA..phi./.phi..DELTA.P, can be found.
Numerous approaches have been taken in the past to provide optical fiber waveguides with coatings either to protect them physically during manufacturing and handling to prevent damage, or to buffer the fiber and isolate it from external forces which would cause signal attenuation. These have included protective coatings of rubber, soft and hard plastics and even metals in various combinations. Aluminum coatings have been utilized for sealing fibers hermetically to preserve their strength, but not to desensitize. Some of the disadvantages of such an arrangement are: (1) The metals have substantially higher thermal expansion coefficient than glass, and therefore, metal coating of glass fibers at high temperature is not possible without causing damage to the glass. Morever, environmental temperature changes induce significant microbending loses in the optical fiber which have been coated with a thick metal jacket. (2) Metals behave elastically over only a limited range of strains and inelastically therebeyond to cause significant microbending loses. (3) Metals exhibit dynamic fatigue when they experience rapidly varying pressures.